THE TRANSPORTATION OF LIQUIDS 137 hydraulic losses in pump = HPw/Eh* It is the indicated pump horsepower, but is difficultly determined on account of the unreliability of pump indicator cards. The brake horsepower, in the case of a power pump, is the horsepower delivered to the pump, as measured by a dynamometer or suitable means. Figure 33 gives the water horsepower and the brake horsepower required at usual quantities and heads For other conditions multiply or divide the horsepower obtained from the diagran proportionately. HPb = HPw/Em(Eh included in Em). Example.The theoretical water horsepower required to pump 500 gal. per minut against 300 ft. head is, as calculated from the indicator diagram, 38.5 horsepower at 80 per cent efficiency the brake horsepower required will be 48 hp. The indicated horsepower, in the case of a steam pump HPt HPw/Em. It i determined from indicator cards taken off the steam end. The input horsepower, in the case of an electrically driven pump, or the electrii horsepower, is the horsepower consumed by the motor, measured at its switchboard In the case of a steam-or air-driven pump, the input horsepower may be based on the steam or air consumption, computed at appropriate quantities per horsepower. Calculation of the Steam End.In computing the size of a crank and flywhee1 pumping engine it is best to find the required indicated horsepower and thei proceed in the usual manner of calculating a steam engine. The reason for this is that usually the steam end consists of a single unit, while the pump end may be composed of a number of pumps, either single- or double-acting. The size may be figured closely, because any lack of power may be made up by a later cutoff. Non-condensing sizes should be figured too small rather than too large, so that there will be no danger o f expanding below the atmospheric line. In a direct-acting steam pump the horsepower can be ignored and the steam piston force F balanced against the plunger load L + the mechanical friction. L = F X Em, where L = area of plunger X total water pressure; F area of steam cylinder X mean effective pressure. In the case of a multi-stage steam end, the mean effective pressure, called pe hereafter, is best referred to the area of the high-pressure cylinder and can be calculated by the following formulas, in which pi = absolute initial pressure in high pressure cylinder; b = back pressure; R = ratio of cylinder areas in a compound pump; and R and RI = the ratios of cylinder areas in a triple expansion pump, R = low pressure area/high pressure area and Rt = low pressure area/high pressure area. Simple steam cylinder direct-acting pumps (so-called high-pressure pumps); pe pi b. Compound pumps: pe 2pt (pi/R) bR; R = \/p/b. Triple expansion pumps: pe = 3pt- (2pi/-\/R) 1>R\; RI = \/(p/b)* and Ri = R2. In these formulas the following values may be substituted: pi = gage pressure at throttle + 10 lb.; b = 16 Ib. for non-condensing, 5 Ib. for condensing compound pumps and 4 lb. for condensing triple expansion pumps. R ^4 for compound pumps . ^ low pressure area /0, , . . . rn, . ,. and R i = L- ii . ----- ^8 for triple-expansion. These values cover unfavorable conditions, such as direct-acting pumps must be designed for. The duty of a pump is its performance based on the output in foot-pounds per 1,000 lb. of dry steam, or per 100 cu. ft. of air, or per 1,000,000 B.t.u. furnished by the boilers at appropriate pressure. The duty of a steam pump can be calculated approximately from the indicator diagram (either actual or ideal) by the formula: card duty = 144,000 pv, and duty = card duty/EmE8 where p = mean effective pressure of whole steam end referred to the area of any one cylinder, v = specific volume of steam at the terminal pressure in this same cylinder, Em = mechanical efficiency, and Es = Steam efficiency, comprising all steam losses.